---
title: "Convert (524)₈ to hexadecimal"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-524-octal-hex"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-524-octal-hex
site: BCT Engineering
---

# Convert (524)₈ to hexadecimal

Digital Logic · Chapter 1: Introduction

- Asked in: 2080 Baisakh, 1.5 marks
- Video: [Hexadecimal to Binary & Binary to Hexadecimal Conversion](https://www.youtube.com/watch?v=WI6Uvci2p7E) — Neso Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/convert-524-octal-hex
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (524)₈ = (?)₁₆.

## Short answer

Write octal 524 as 3-bit binary groups: 101 010 100₂. Regroup into 4-bit nibbles: 0001 0101 0100₂, which is (154)₁₆.

## Answer

Convert octal to binary (3 bits per digit), then regroup in 4 bits from the right.

5 = 101, 2 = 010, 4 = 100 → $(101\ 010\ 100)_2$

Regroup: $0001\ 0101\ 0100$ → 1 5 4

Check: $(524)_8 = 5\times64 + 2\times8 + 4 = 340$, and $(154)_{16} = 256 + 80 + 4 = 340$.

**Answer: $(524)_8 = (154)_{16}$**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How to convert octal to hex?
   A. Divide by 8
   B. Octal to 3-bit binary, regroup in 4 bits
   C. Directly map digits
   D. Multiply by 16
   Answer: B. Binary is the common base. (Key point: Method)

2. (524) octal in binary?
   A. 101 100 010
   B. 110 010 100
   C. 101 010 100
   D. 101 010 010
   Answer: C. 5=101, 2=010, 4=100. (Key point: Binary form)

3. (524) octal in hex?
   A. 524
   B. 1A4
   C. 254
   D. 154
   Answer: D. 0001 0101 0100. (Key point: Final answer)

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